The equation of a circle $C$ is $x^2+y^2+10x+4y-7 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Answer: To find the equation in standard form, complete the square. $(x^2+10x) + (y^2+4y) = 7$ $(x^2+10x+25) + (y^2+4y+4) = 7 + 25 + 4$ $(x+5)^{2} + (y+2)^{2} = 36 = 6^2$ Thus, $(h, k) = (-5, -2)$ and $r = 6$.